Suppose that the system x' = Ax + g(x) is locally linear near the O as x → 0, and that A is a 2 x 2 matrix lg(x)|| || origin, so that with purely imaginary eigenvalues ±iµ. Which of the following must be true about this system?

Suppose that the system x' = Ax + g(x) is locally linear near the O as x → 0, and that A is a 2 x 2 matrix lg(x)|| || origin, so that with purely imaginary eigenvalues ±iµ. Which of the following must be true about this system?

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

Suppose that the system x' = Ax + g(x) is locally linear near the
O as x → 0, and that A is a 2 x 2 matrix
llg(x)||
||||
origin, so that
with purely imaginary eigenvalues ±iµ. Which of the following must
be true about this system?
(0,0) is a critical point.
(0,0) is stable.
(0,0) is unstable.
(0,0) is a spiral point.
(0,0) is a node.
(0,0) is asymptotically stable.
(0,0) is a saddle point.
(0,0) is a center.

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